Finite Group Databasebeta

← D5×#4844 #14425944

Subgroups — D5×#4844 #14425944

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×D24C211yesmaximal, characteristic
2C2×D5×#204C211yesmaximal, characteristic, complemented
3D5×#875C211yesmaximal, characteristic, complemented
4C4×D5×D12C211yesmaximal, characteristic, complemented
5#11750945C211yesmaximal, characteristic, complemented
6C5×#4844C211yesmaximal, characteristic, complemented
7C3×D5×C4⋊C8C211yesmaximal, characteristic, complemented
8D5×#821C211yesmaximal, characteristic, complemented
9#11747779C211yesmaximal, characteristic, complemented
10#11747777C211yesmaximal, characteristic, complemented
11#11747774C211yesmaximal, characteristic, complemented
12#11747770C211yesmaximal, characteristic, complemented
13D5×#816C211yesmaximal, characteristic, complemented
14#11747046C211yesmaximal, characteristic, complemented
15#11747038C211yesmaximal, characteristic, complemented
16D5×#463—31nomaximal, Hall
17C2×D5×D12C2211yescharacteristic
18C2×D5×D12C2211yescharacteristic
19C2×C4×D3×D5—21no—
20C2×D5×Dic6C2211yescharacteristic
21C2×D120C2211yescharacteristic
22C2×#6706C2211yescharacteristic, complemented
23#91764C2211yescharacteristic, complemented
24C4×D60C2211yescharacteristic, complemented
25C2×C5×D24C2211yescharacteristic
26C2×C5×#204C2211yescharacteristic, complemented
27C5×#875C2211yescharacteristic, complemented
28C4×C5×D12C2211yescharacteristic, complemented
29C2×C3×C8×D5C2211yescharacteristic
30C2×C3×C8×D5C2211yescharacteristic
31C3×C42×D5C2211yescharacteristic
32D5×(C2×D3)⋊C4—21no—
33D5×(C2×D3)⋊C4—21no—
34D5×(C2×D3)⋊C4—21no—
35C4×#1203—21no—
36#91418C2211yescharacteristic, complemented
37Dic5×D12C2211yescharacteristic, complemented
38D5×C4⋊Dic3C2211yescharacteristic
39#91405—21no—
40#91375C2211yescharacteristic, complemented
41#91373C2211yescharacteristic, complemented
42#91350—21no—
43#91350—21no—
44C2×#6660C2211yescharacteristic, complemented
45C2×#6659C2211yescharacteristic, complemented
46C2×#6654C2211yescharacteristic
47C2×#6654C2211yescharacteristic
48D5×D24—24no—
49D5×#204—24no—
50C3×C5×C4⋊C8C2211yescharacteristic, complemented
51#91105C2211yescharacteristic, complemented
52#91100C2211yescharacteristic, complemented
53C5×#821C2211yescharacteristic, complemented
54C5×#816C2211yescharacteristic, complemented
55C3×#3946C2211yescharacteristic, complemented
56C3×#3946C2211yescharacteristic, complemented
57C3×C4⋊#168C2211yescharacteristic, complemented
58#90975C2211yescharacteristic, complemented
59#90973C2211yescharacteristic, complemented
60#90969C2211yescharacteristic, complemented
61#90967C2211yescharacteristic, complemented
62C2×#4844—51nomaximal, Hall
63C2×D5×SD16—31no—
64C2×D5×D8—31no—
65D5×#124—31no—
66C4×D4×D5—31no—
67C5×#463—31no—
68#65454—31no—
69#65442—31no—
70#65346—31no—
71#65305—31no—
72#65133—31no—
73D5×C4⋊C8D311yescharacteristic, complemented
74#65108—31no—
75D5×#103—31no—
76#65076—31no—
77D5×#102—31no—
78C22×D3×D5—21no—
79C22×D3×D5—21no—
80C2×D60C2311yescharacteristic
81C2×D60C2311yescharacteristic
82C2×C4×D15—21no—
83C2×Dic30C2311yescharacteristic
84C2×C5×D12C2311yescharacteristic
85C2×C5×D12C2311yescharacteristic
86C2×C4×C5×D3—21no—
87C2×C5×Dic6C2311yescharacteristic
88C2×C3×C4×D5D411yescharacteristic
89C2×C3×C4×D5D411yescharacteristic
90C2×C3×C4×D5C2311yescharacteristic
91C2×#1204—21no—
92C2×#1203—21no—
93C2×#1203—21no—
94C2×#1200—21no—
95C2×D3×Dic5—21no—
96C2×D5×Dic3—21no—
97C2×D5×Dic3—21no—
98D5×D12—22no—
99D5×D12—22no—
100D5×D12—22no—
101D5×D12D414yes—
102C4×D3×D5—44no—
103D5×Dic6—22no—
104D5×Dic6—22no—
105C2×C3×C5×C8C2311yescharacteristic
106C2×C3×C5×C8C2311yescharacteristic
107C3×C42×C5C2311yescharacteristic
108#6714—21no—
109#6714—21no—
110#6714—21no—
111C4⋊Dic15C2311yescharacteristic
112D120—22no—
113#6706—22no—
114C5×(C2×D3)⋊C4—21no—
115C5×(C2×D3)⋊C4—21no—
116C5×(C2×D3)⋊C4—21no—
117C5×C4⋊Dic3C2311yescharacteristic
118C5×D24—22no—
119C5×#204—22no—
120C3×C4×Dic5D411yescharacteristic
121C3×C4×Dic5D411yescharacteristic
122C3×C4×Dic5C2311yescharacteristic
123C2×C3×#168C2311yescharacteristic
124C2×C3×#168C2311yescharacteristic
125C3×C8×D5—22no—
126C3×C8×D5—22no—
127#6668—21no—
128#6667—21no—
129#6667—21no—
130#6667—21no—
131(C2×D3)⋊Dic5—21no—
132(C2×D3)⋊Dic5—21no—
133(C2×D3)⋊Dic5—21no—
134#6660—22no—
135#6659—22no—
136#6654—22no—
137#6654—22no—
138C22×D24—51no—
139C22×#204—51no—
140C2×#875—51no—
141C2×C4×D12—51no—
142C2×C3×C4⋊C8—51no—
143C2×#821—51no—
144C2×#816—51no—
145#4844—51no—
146#4844—51no—
147#4844—51no—
148#4844—51no—
149#4844—51no—
150#4844—51no—
151#4844—51no—
152#4844D511yescharacteristic, direct product factor
153C2×Q8×D5—31no—
154C2×D4×D5—31no—
155C2×D4×D5—31no—
156C22×C4×D5—61no—
157C2×C5×SD16—31no—
158C2×C5×D8—31no—
159C5×#124—31no—
160C4×C5×D4—31no—
161#4093—31no—
162C2×#688—31no—
163#4082—31no—
164D4×Dic5—31no—
165C2×#687—31no—
166C2×#686—31no—
167C2×#686—31no—
168C4×C22⋊D5—61no—
169D5×SD16—64no—
170D5×D8—64no—
171C2×D40—31no—
172C2×#677—31no—
173C2×C8×D5C2×D311yescharacteristic
174C2×C8×D5C2×D311yescharacteristic
175#4039—31no—
176D5×C4⋊C4—31no—
177#4031—61no—
178#4031—61no—
179#4027—61no—
180D5×C22⋊C4—61no—
181D5×C22⋊C4—61no—
182D5×C22⋊C4—61no—
183#4021—31no—
184C4×D20—31no—
185C42×D5C2×D311yescharacteristic
186C5×C4⋊C8C2×D311yescharacteristic, complemented
187C5×#103—31no—
188C5×#102—31no—
189#3967—31no—
190#3964—31no—
191#3953—31no—
192#3948—31no—
193#3946C2×D311yescharacteristic, complemented
194#3946C2×D311yescharacteristic, complemented
195#3942—31no—
196#3941—31no—
197C4⋊#168C2×D311yescharacteristic, complemented
198C2×#463—151noSylow
199C22×D15—21no—
200C22×D15—21no—
201C22×C5×D3—21no—
202C22×C5×D3—21no—
203C22×C3×D5C2×D411yescharacteristic
204C2×D3×D5—24no—
205C2×D3×D5—42no—
206C2×D3×D5—42no—
207C2×D3×D5—42no—
208C2×D3×D5—42no—
209C2×D3×D5—42no—
210C2×C3×C4×C5C2×D411yescharacteristic
211C2×C3×C4×C5C2×D411yescharacteristic
212C2×C3×C4×C5C2411yescharacteristic
213C2×Dic15—21no—
214C2×Dic15—21no—
215D60—21no—
216D60—21no—
217D60—21no—
218D60C2×D412yes—
219C4×D15—42no—
220Dic30—21no—
221Dic30—21no—
222C2×C5×Dic3—21no—
223C2×C5×Dic3—21no—
224C5×D12—21no—
225C5×D12—21no—
226C5×D12—21no—
227C5×D12C2×D412yes—
228C4×C5×D3—42no—
229C5×Dic6—21no—
230C5×Dic6—21no—
231C2×C3×Dic5C2×D411yescharacteristic
232C2×C3×Dic5C2×D411yescharacteristic
233C2×C3×Dic5C2×D411yescharacteristic
234C3×C4×D5—22no—
235C3×C4×D5—22no—
236C3×C4×D5C2×D412yes—
237C3×C4×D5#4112yes—
238#1204—42no—
239#1203—24no—
240#1203—42no—
241#1200—42no—
242D3×Dic5—42no—
243D5×Dic3—42no—
244D5×Dic3—42no—
245C3×C5×C8—21no—
246C3×C5×C8—21no—
247C3×#168—21no—
248C3×#168—21no—
249C22×D12—51no—
250C22×D12—51no—
251C22×C4×D3—101no—
252C22×Dic6—51no—
253C22×C3×C8—51no—
254C22×C3×C8—51no—
255C2×C3×C42—51no—
256C2×(C2×D3)⋊C4—101no—
257C2×(C2×D3)⋊C4—101no—
258C2×(C2×D3)⋊C4—101no—
259C2×C4⋊Dic3—51no—
260C2×D24—51no—
261C2×D24—51no—
262C2×D24—51no—
263C2×D24—104no—
264C2×D24C2×D511yescharacteristic
265C2×#204—51no—
266C2×#204—51no—
267C2×#204—51no—
268C2×#204—104no—
269C2×#204C2×D511yescharacteristic, complemented
270#875—51no—
271#875—51no—
272#875—51no—
273#875—101no—
274#875—101no—
275#875C2×D511yescharacteristic, complemented
276C4×D12—51no—
277C4×D12—51no—
278C4×D12—51no—
279C4×D12—101no—
280C4×D12—101no—
281C4×D12C2×D511yescharacteristic, complemented
282C3×C4⋊C8—51no—
283C3×C4⋊C8—51no—
284C3×C4⋊C8—51no—
285C3×C4⋊C8C2×D511yescharacteristic, complemented
286#821—51no—
287#821—51no—
288#821—51no—
289#821C2×D511yescharacteristic, complemented
290#816—51no—
291#816—51no—
292#816—51no—
293#816C2×D511yescharacteristic, complemented
294C23×D5—61no—
295C23×D5—61no—
296C2×C5×Q8—31no—
297C2×C5×D4—31no—
298C2×C5×D4—31no—
299C22×C4×C5—61no—
300C2×C22⋊D5—61no—
301C2×C22⋊D5—61no—
302C22×Dic5—61no—
303Q8×D5—62no—
304Q8×D5—62no—
305D4×D5—34no—
306D4×D5—62no—
307D4×D5—62no—
308D4×D5—62no—
309C2×D20—31no—
310C2×D20—31no—
311C2×C4×D5—61no—
312C2×C4×D5—61no—
313C2×C4×D5—61no—
314C2×C4×D5—61no—
315C2×C4×D5—124no—
316C2×C4×D5D1211yescharacteristic
317C2×C4×D5D1211yescharacteristic
318C2×C4×D5C22×D311yescharacteristic
319C2×Dic10—31no—
320C2×Dic10—61no—
321C5×SD16—62no—
322C5×D8—62no—
323C2×C5×C8C22×D311yescharacteristic
324C2×C5×C8C22×D311yescharacteristic
325C5×C4⋊C4—31no—
326C5×C22⋊C4—61no—
327C5×C22⋊C4—61no—
328C5×C22⋊C4—61no—
329C42×C5C22×D311yescharacteristic
330C22⋊Dic5—61no—
331C22⋊Dic5—61no—
332C22⋊Dic5—61no—
333#688—62no—
334#687—62no—
335#686—62no—
336#686—62no—
337#685—61no—
338#685—61no—
339#685—61no—
340#685—61no—
341#685—61no—
342#685—61no—
343C4⋊Dic5—31no—
344#683—61no—
345C4×Dic5D1211yescharacteristic
346C4×Dic5D1211yescharacteristic
347C4×Dic5C22×D311yescharacteristic
348C2×#168C22×D311yescharacteristic
349C2×#168C22×D311yescharacteristic
350D40—62no—
351#677—62no—
352C8×D5—22no—
353C8×D5—22no—
354C22×SD16—151no—
355C22×D8—151no—
356C2×#124—151no—
357C2×C4×D4—151no—
358#463—31no—
359#463—151no—
360#463—151no—
361#463—151no—
362#463—151no—
363#463—151no—
364#463—151no—
365#463—151no—
366C2×C4⋊C8—51no—
367C2×#103—151no—
368C2×#102—151no—
369C22×C3×C5C22×D411yescharacteristic
370C2×D15—22no—
371C2×D15—41no—
372C2×D15—41no—
373C2×D15—41no—
374C2×D15—41no—
375C2×D15—41no—
376C2×C5×D3—22no—
377C2×C5×D3—41no—
378C2×C5×D3—41no—
379C2×C5×D3—41no—
380C2×C5×D3—41no—
381C2×C5×D3—41no—
382C2×C3×D5#12112yes—
383C2×C3×D5#13512yes—
384C2×C3×D5AGL(1,ℤ/8)12yes—
385D3×D5—48no—
386D3×D5—84no—
387C3×C4×C5—21no—
388C3×C4×C5—21no—
389C3×C4×C5C22×D411yescharacteristic
390C3×C4×C5C2×#4111yescharacteristic
391Dic15—41no—
392Dic15—41no—
393C3×Dic5—21no—
394C3×Dic5—21no—
395C3×Dic5#12112yes—
396C5×Dic3—41no—
397C5×Dic3—41no—
398C23×D3—101no—
399C23×D3—101no—
400C22×C3×C4—51no—
401C22×C3×C4—51no—
402C22×C3×C4—51no—
403C22×Dic3—101no—
404C22×Dic3—101no—
405C2×D12—51no—
406C2×D12—54no—
407C2×D12—51no—
408C2×D12—102no—
409C2×D12—102no—
410C2×D12—102no—
411C2×D12—101no—
412C2×D12—101no—
413C2×D12C22×D511yescharacteristic
414C2×D12C22×D511yescharacteristic
415C2×C4×D3—21no—
416C2×C4×D3—101no—
417C2×C4×D3—101no—
418C2×C4×D3—101no—
419C2×C4×D3—204no—
420C2×Dic6—51no—
421C2×Dic6—102no—
422C2×Dic6—102no—
423C2×Dic6—101no—
424C2×Dic6C22×D511yescharacteristic
425C2×C3×C8—51no—
426C2×C3×C8—51no—
427C2×C3×C8—102no—
428C2×C3×C8—102no—
429C2×C3×C8C22×D511yescharacteristic
430C2×C3×C8C22×D511yescharacteristic
431C3×C42—51no—
432C3×C42—51no—
433C3×C42—51no—
434C3×C42C22×D511yescharacteristic
435(C2×D3)⋊C4—21no—
436(C2×D3)⋊C4—21no—
437(C2×D3)⋊C4—21no—
438(C2×D3)⋊C4—101no—
439(C2×D3)⋊C4—101no—
440(C2×D3)⋊C4—101no—
441(C2×D3)⋊C4—101no—
442(C2×D3)⋊C4—101no—
443(C2×D3)⋊C4—101no—
444(C2×D3)⋊C4—101no—
445(C2×D3)⋊C4—101no—
446(C2×D3)⋊C4—101no—
447C4⋊Dic3—51no—
448C4⋊Dic3—101no—
449C4⋊Dic3C22×D511yescharacteristic
450D24—22no—
451D24—102no—
452D24—102no—
453D24—102no—
454#204—22no—
455#204—102no—
456#204—102no—
457#204—102no—
458C23×C5—61no—
459C23×C5—61no—
460C22×D5—61no—
461C22×D5—64no—
462C22×D5—61no—
463C22×D5—122no—
464C22×D5—122no—
465C22×D5—122no—
466C22×D5—122no—
467C22×D5—122no—
468C22×D5C2×D1211yescharacteristic
469C5×Q8—61no—
470C5×Q8—61no—
471C5×D4—32no—
472C5×D4—61no—
473C5×D4—61no—
474C5×D4—61no—
475C2×C4×C5—61no—
476C2×C4×C5—61no—
477C2×C4×C5—122no—
478C2×C4×C5C2×D1211yescharacteristic
479C2×C4×C5C2×D1211yescharacteristic
480C2×C4×C5C23×D311yescharacteristic
481C22⋊D5—64no—
482C22⋊D5—122no—
483C2×Dic5—61no—
484C2×Dic5—61no—
485C2×Dic5—122no—
486C2×Dic5C2×D1211yescharacteristic
487C2×Dic5C2×D1211yescharacteristic
488C2×Dic5C2×D1211yescharacteristic
489D20—32no—
490D20—61no—
491D20—61no—
492D20—61no—
493C4×D5—22no—
494C4×D5—22no—
495C4×D5—122no—
496C4×D5—122no—
497C4×D5—122no—
498C4×D5—122no—
499C4×D5D3×D412yes—
500C4×D5#23912yes—
501Dic10—61no—
502Dic10—61no—
503Dic10—122no—
504C5×C8—21no—
505C5×C8—21no—
506#168—21no—
507#168—21no—
508C22×Q8—151no—
509C22×D4—151no—
510C22×D4—151no—
511C23×C4—301no—
512C2×SD16—31no—
513C2×SD16—151no—
514C2×SD16—151no—
515C2×SD16—151no—
516C2×SD16—304no—
517C2×D8—31no—
518C2×D8—151no—
519C2×D8—151no—
520C2×D8—151no—
521C2×D8—304no—
522C22×C8—51no—
523C22×C8—51no—
524#124—31no—
525#124—151no—
526#124—151no—
527#124—151no—
528#124—301no—
529#124—301no—
530C4×D4—31no—
531C4×D4—151no—
532C4×D4—151no—
533C4×D4—151no—
534C4×D4—301no—
535C4×D4—301no—
536C2×C4⋊C4—151no—
537C2×C22⋊C4—301no—
538C2×C22⋊C4—301no—
539C2×C22⋊C4—301no—
540C2×C42—51no—
541C4⋊C8—51no—
542C4⋊C8—51no—
543C4⋊C8—51no—
544C4⋊C8D3×D511yescharacteristic, complemented
545#103—31no—
546#103—151no—
547#103—151no—
548#103—151no—
549#102—31no—
550#102—151no—
551#102—151no—
552#102—151no—
553C2×C3×C5C2×#12111yescharacteristic
554C2×C3×C5C2×#13511yescharacteristic
555C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
556D15—42no—
557D15—81no—
558C3×D5#46314yescomplemented
559C5×D3—42no—
560C5×D3—81no—
561C23×C3—51no—
562C22×D3—21no—
563C22×D3—21no—
564C22×D3—104no—
565C22×D3—101no—
566C22×D3—101no—
567C22×D3—202no—
568C22×D3—202no—
569C22×D3—202no—
570C22×D3—202no—
571C22×D3—202no—
572C2×C3×C4—51no—
573C2×C3×C4—52no—
574C2×C3×C4—52no—
575C2×C3×C4—51no—
576C2×C3×C4—51no—
577C2×C3×C4—102no—
578C2×C3×C4—102no—
579C2×C3×C4D4×D511yescharacteristic
580C2×C3×C4D4×D511yescharacteristic
581C2×C3×C4C23×D511yescharacteristic
582C2×Dic3—21no—
583C2×Dic3—21no—
584C2×Dic3—101no—
585C2×Dic3—101no—
586C2×Dic3—202no—
587C2×Dic3—202no—
588D12—21no—
589D12—21no—
590D12—21no—
591D12—52no—
592D12—104no—
593D12—101no—
594D12—101no—
595D12—101no—
596D12—202no—
597D12D4×D512yes—
598C4×D3—42no—
599C4×D3—202no—
600C4×D3—202no—
601C4×D3—202no—
602Dic6—21no—
603Dic6—21no—
604Dic6—101no—
605Dic6—101no—
606Dic6—202no—
607C3×C8—21no—
608C3×C8—21no—
609C3×C8—101no—
610C3×C8—101no—
611C22×C5—62no—
612C22×C5—121no—
613C22×C5—121no—
614C22×C5—121no—
615C22×C5—121no—
616C22×C5—121no—
617C22×C5C22×D1211yescharacteristic
618C2×D5—62no—
619C2×D5—121no—
620C2×D5—121no—
621C2×D5—128no—
622C2×D5—121no—
623C2×D5—121no—
624C2×D5—121no—
625C2×D5—244no—
626C2×D5#89512yes—
627C2×D5#90412yes—
628C2×D5#90812yes—
629C4×C5—21no—
630C4×C5—21no—
631C4×C5—121no—
632C4×C5—121no—
633C4×C5C2×D3×D411yescharacteristic
634C4×C5C2×#23911yescharacteristic
635Dic5—21no—
636Dic5—21no—
637Dic5—121no—
638Dic5—121no—
639Dic5#89512yes—
640C24—301no—
641C24—301no—
642C2×Q8—31no—
643C2×Q8—151no—
644C2×Q8—301no—
645C2×Q8—302no—
646C2×Q8—302no—
647C2×D4—31no—
648C2×D4—31no—
649C2×D4—154no—
650C2×D4—151no—
651C2×D4—151no—
652C2×D4—302no—
653C2×D4—302no—
654C2×D4—302no—
655C2×D4—301no—
656C2×D4—301no—
657C22×C4—51no—
658C22×C4—51no—
659C22×C4—51no—
660C22×C4—61no—
661C22×C4—301no—
662C22×C4—301no—
663C22×C4—301no—
664C22×C4—301no—
665C22×C4—301no—
666C22×C4—604no—
667SD16—62no—
668SD16—302no—
669SD16—302no—
670SD16—302no—
671D8—62no—
672D8—302no—
673D8—302no—
674D8—302no—
675C2×C8—51no—
676C2×C8—51no—
677C2×C8—102no—
678C2×C8—102no—
679C2×C8C2×D3×D511yescharacteristic
680C2×C8C2×D3×D511yescharacteristic
681C4⋊C4—31no—
682C4⋊C4—151no—
683C4⋊C4—301no—
684C22⋊C4—61no—
685C22⋊C4—61no—
686C22⋊C4—61no—
687C22⋊C4—301no—
688C22⋊C4—301no—
689C22⋊C4—301no—
690C22⋊C4—301no—
691C22⋊C4—301no—
692C22⋊C4—301no—
693C22⋊C4—301no—
694C22⋊C4—301no—
695C22⋊C4—301no—
696C42—51no—
697C42—51no—
698C42—51no—
699C42C2×D3×D511yescharacteristic
700C3×C5C2×#46311yescharacteristic, complemented, Hall
701C22×C3—52no—
702C22×C3—52no—
703C22×C3—52no—
704C22×C3C2×D4×D511yescharacteristic
705C2×D3—22no—
706C2×D3—41no—
707C2×D3—41no—
708C2×D3—41no—
709C2×D3—41no—
710C2×D3—41no—
711C2×D3—102no—
712C2×D3—208no—
713C2×D3—201no—
714C2×D3—201no—
715C2×D3—201no—
716C2×D3—201no—
717C2×D3—201no—
718C2×D3—404no—
719C3×C4—21no—
720C3×C4—21no—
721C3×C4—52no—
722C3×C4—101no—
723C3×C4—101no—
724C3×C4C2×D4×D511yescharacteristic
725C3×C4D5×#4111yescharacteristic
726Dic3—41no—
727Dic3—41no—
728Dic3—201no—
729Dic3—201no—
730C2×C5—122no—
731C2×C5—241no—
732C2×C5C2×#89511yescharacteristic
733C2×C5C2×#90411yescharacteristic
734C2×C5C2×#90811yescharacteristic
735D5—122no—
736D5—241no—
737D5#484414yesdirect product factor
738C23—51no—
739C23—61no—
740C23—61no—
741C23—304no—
742C23—301no—
743C23—301no—
744C23—602no—
745C23—602no—
746C23—602no—
747C23—602no—
748C23—602no—
749Q8—61no—
750Q8—61no—
751Q8—301no—
752Q8—301no—
753Q8—602no—
754D4—32no—
755D4—61no—
756D4—61no—
757D4—61no—
758D4—152no—
759D4—304no—
760D4—301no—
761D4—301no—
762D4—301no—
763D4—602no—
764C2×C4—51no—
765C2×C4—52no—
766C2×C4—52no—
767C2×C4—51no—
768C2×C4—51no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—102no—
772C2×C4—102no—
773C2×C4—122no—
774C2×C4—301no—
775C2×C4—301no—
776C2×C4—602no—
777C2×C4—602no—
778C2×C4—602no—
779C2×C4—602no—
780C2×C4—602no—
781C2×C4D5×D1211yescharacteristic
782C2×C4D5×D1211yescharacteristic
783C2×C4C22×D3×D511yescharacteristic
784C8—21no—
785C8—21no—
786C8—101no—
787C8—101no—
788C2×C3—54no—
789C2×C3D5×#12111yescharacteristic
790C2×C3D5×#13511yescharacteristic
791C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
792D3—42no—
793D3—81no—
794D3—202no—
795D3—401no—
796C5C2×#484411yescharacteristic, complemented, Sylow
797C22—52no—
798C22—52no—
799C22—52no—
800C22—62no—
801C22—121no—
802C22—121no—
803C22—121no—
804C22—121no—
805C22—121no—
806C22—302no—
807C22—608no—
808C22—601no—
809C22—601no—
810C22—601no—
811C22—601no—
812C22—601no—
813C22—1204no—
814C22C2×D5×D1211yescharacteristic
815C4—21no—
816C4—21no—
817C4—52no—
818C4—101no—
819C4—101no—
820C4—121no—
821C4—121no—
822C4—601no—
823C4—601no—
824C4D3×D4×D511yescharacteristic
825C4D5×#23911yescharacteristic
826C3D5×#46311yescharacteristic, complemented, Sylow
827C2—54no—
828C2—122no—
829C2—241no—
830C2—602no—
831C2—1201no—
832C2D5×#89511yescharacteristic
833C2D5×#90411yescharacteristic
834C2D5×#90811yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C22×D4
prime radicalC2×D5×D24C2
hypercenterC4⋊C8D3×D5
hypocenterC3×C5C2×#463
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×D5×#204C2semidirect
3. D5×#875C2semidirect
4. C4×D5×D12C2semidirect
5. #11750945C2semidirect
6. C5×#4844C2semidirect
7. C3×D5×C4⋊C8C2semidirect
8. D5×#821C2semidirect
9. #11747779C2semidirect
10. #11747777C2semidirect
11. #11747774C2semidirect
12. #11747770C2semidirect
13. D5×#816C2semidirect
14. #11747046C2semidirect
15. #11747038C2semidirect
22. C2×#6706C22semidirect
23. #91764C22semidirect
24. C4×D60C22semidirect
26. C2×C5×#204C22semidirect
27. C5×#875C22semidirect
28. C4×C5×D12C22semidirect
36. #91418C22semidirect
37. Dic5×D12C22semidirect
40. #91375C22semidirect
41. #91373C22semidirect
44. C2×#6660C22semidirect
45. C2×#6659C22semidirect
50. C3×C5×C4⋊C8C22semidirect
51. #91105C22semidirect
52. #91100C22semidirect
53. C5×#821C22semidirect
54. C5×#816C22semidirect
55. C3×#3946C22semidirect
56. C3×#3946C22semidirect
57. C3×C4⋊#168C22semidirect
58. #90975C22semidirect
59. #90973C22semidirect
60. #90969C22semidirect
61. #90967C22semidirect
73. D5×C4⋊C8D3semidirect
152. #4844D5direct (N × H)
186. C5×C4⋊C8C2×D3semidirect
193. #3946C2×D3semidirect
194. #3946C2×D3semidirect
197. C4⋊#168C2×D3semidirect
269. C2×#204C2×D5semidirect
275. #875C2×D5semidirect
281. C4×D12C2×D5semidirect
285. C3×C4⋊C8C2×D5semidirect
289. #821C2×D5semidirect
293. #816C2×D5semidirect
544. C4⋊C8D3×D5semidirect
558. C3×D5#463semidirect
700. C3×C5C2×#463semidirect
737. D5#4844direct (N × H)
796. C5C2×#4844semidirect
826. C3D5×#463semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×D5×D242
C2×D5×#2042
D5×#8752
C4×D5×D122
#117509452
C5×#48442
C3×D5×C4⋊C82
D5×#8212
#117477792
#117477772
#117477742
#117477702
D5×#8162
#117470462
#117470382
D5×#4633
C2×#48445